Twenty Questions Information Theory Girls Engaged in Math and Science, June 2012

Twenty Questions Information Theory

Who can read these sentences? pls txt tmrw. ths sntnce hs th vwls mssng Why are we able to read these sentences when some of the letters are missing?

There is not a lot of “information” in vowels. Which has more information: A. A 1,000 page telephone book B. A 1,000 page book of blank paper C. Tolkien’s Lord of the Rings

What is information? How can we measure the amount of information in a book? Is the number of pages or the number of words important? Can one book have more information than another? What if it is a very boring book or a particularly interesting one? What if there was a book that only contained the words, “blah blah blah blah.” Would that book contain more or less information than a dictionary?

Computer Scientists measure information by how surprising a message is. Telling you something that you know already—for example, when a friend who always walks to school says “I walked to school today”—doesn’t give you any information, because it isn’t surprising. If your friend said instead, “I got a ride to school in a helicopter today,” that would be surprising, and would therefore tell us a lot of information.

How can surprise be measured? Surprise can be measured by trying to guess the information and seeing how difficult it is. If your friend says, “Guess how I got to school today,” and they had walked, you would probably guess right the first time. It might take a few more guesses before you got to a helicopter, and even more if they had travelled by spaceship.

Your turn! We’re going to play 20 questions as a group. Find a partner you’ve never met before, and decide who will ask the questions and who will answer them. If you’re the one thinking up the mystery item, try to think of an item that contains a lot of information-- in other words, something surprising. If you are guessing, try to think of things that require a lot of information and choose your guesses carefully!

In your game: Count the number of questions that were asked. This is a measure of the value of the “information”. If you have time, switch roles and play again. Be sure to think about the guessing strategy and when you’re done, we’ll discuss your strategies.

Discussion What strategies did you use? Which were the best? How can you measure which strategies were the most effective?